Epidemiology and Health Geography
Studying how diseases spread through populations and the geography of healthcare access.
Key Questions
- Analyze how globalization accelerates the spread of pandemics.
- Explain what a 'food desert' is and how it affects public health.
- Predict why certain diseases persist in specific geographic regions.
Common Core State Standards
About This Topic
Interpreting residuals is the final step in validating a linear model. A residual is the difference between the actual observed value and the value predicted by the line of best fit. In 9th grade, students learn to create 'residual plots' to determine if a linear model is actually appropriate for the data. This is a sophisticated Common Core standard that moves students toward high-level statistical thinking.
If a residual plot shows a random scatter of points, the linear model is a good fit. However, if the residuals show a clear pattern (like a U-shape), it suggests that a non-linear model (like a quadratic) would be better. This topic comes alive when students can use collaborative investigations to 'audit' their own models, using residuals to prove whether their predictions are trustworthy or if they need a different mathematical approach.
Active Learning Ideas
Inquiry Circle: The Model Audit
Groups are given a data set and a 'proposed' linear model. They must calculate the residuals for each point and create a residual plot. They then act as 'auditors' to decide if the linear model should be 'accepted' or 'rejected' based on the pattern of the residuals.
Think-Pair-Share: Pattern or Random?
Show three different residual plots: one random, one curved, and one with a 'fan' shape. Pairs must discuss what each plot tells them about the original data and why a random scatter is the 'gold standard' for a linear fit.
Simulation Game: Predicting with Error
Students use a linear model to predict a result (e.g., how many rubber bands it takes to drop a 'bungee' doll safely). They perform the experiment, calculate the residual (the error), and discuss how they could adjust their model to reduce the residual next time.
Watch Out for These Misconceptions
Common MisconceptionStudents often think a 'pattern' in a residual plot is a good thing because patterns are usually good in math.
What to Teach Instead
Use the 'Model Audit' activity. Peer discussion helps students realize that a pattern in the 'error' (residuals) means the model is consistently missing something, which is a sign that the model is wrong.
Common MisconceptionBelieving that a high r-value means you don't need to check the residuals.
What to Teach Instead
Show a data set that is slightly curved but still has a high r-value. Collaborative analysis of the residual plot will reveal the curve that the r-value missed, proving that residuals are the 'final word' on model fit.
Suggested Methodologies
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Frequently Asked Questions
What is a residual plot?
How can active learning help students understand residuals?
What does a 'U-shaped' residual plot mean?
Can a residual be negative?
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